Tony Blair's government last night braced itself for the unknown terrain of a second Bush administration in the White House five weeks after spin doctors in Downing Street, the Treasury and the Foreign Office first rehearsed mood music that was optimistic - possibly too optimistic.

"It will make no difference who wins. George W Bush has a lot of good people around him," one senior aide to Tony Blair insisted as the votes were being counted on November 7. That line has not changed.

At breakfast time on November 8 Robin Cook, the for eign secretary, said: "I congratulate George Bush if it is confirmed that he has won and we look forward to working with him and keeping Britain as that unique bridge between America and Europe."

He will say much the same this morning. As for the kind of ideological differences that may rend asunder the cosy relationship between London and Washington in the Clinton-Blair era, Mr Cook said at the time: "I'm not the slightest [bit] worried. George Bush is firmly within the mainstream of American foreign policy, American tradition."

Privately, officials confirmed that upbeat view last night. In international affairs, one said, the Foreign Office expects a Bush administration to be "very much part of the internationally outward-looking post-war consensus".

That may be optimistic. Mr Bush does indeed have good staff, many inherited from his father. But they are also veterans of the cold war world whose instincts have become "unilateralist" rather than "isolationist".

General Colin Powell, the son of poor immigrants from Jamaica whom Mr Cook met last winter, fits that mould. A Vietnam veteran, he does not like to put US troops in harm's way without good reason.

Ground troops in Kosovo may not meet that test, as senior Bush staffers hinted during the US campaign. Bill Clinton also played that card in 1992, leading Whitehall officials to argue: "It's just politics."

Some were quick to point out that a conservative White House which supports Labour's drive to beef up EU defence capacity (the best way to lock in the US commitment to Nato, Cook insists) will be a plus, and unhelpful to William Hague's campaign against the EU rapid reaction force.

As for the "third way" politics which made Tony Blair's relationship with the Rhodes scholar from Arkansas so "intense", they are more prob lematical. But New Labour strategists dismiss the idea that Mr Bush's narrow, disputed win amounts to much of a boost for Mr Hague.

"The manner of his victory diminishes the degree to which rightwing newspapers can claim the zeitgeist is flowing back to the centre-right," one of Gordon Brown's lieutenants said yesterday. In that regard Labour's cheerful pre-election whistling is probably warranted.

Mr Hague visited Mr Bush in Texas and enthusiastically embraced his slogan of "compassionate conservatism". But he has not moved into Governor Bush's centre-ground, preferring since mid-1999 to embrace the more rightwing stance of Mike Harris, the premier of Ontario whose "common sense revolution" on tax and social policy Mr Hague rapidly devoured.

Unlike Vice-President Al Gore, Tony Blair does not have to get out of anyone's shadow. "I am my own man," Mr Gore was still asserting as late as August. That problem prevented him proclaiming the Clinton economic record or using the Clinton campaign magic.

Mr Blair and Mr Brown will not make that mistake. Nor did they interfere in the election in the foolish way some Tory officials did to help Bush Snr against Mr Clinton (over his military draft record) in 1992.

That soured relations and impacted seriously on the Northern Ireland peace process from 1992-97, the only time London and Washington have been badly at odds since the Nixon-Heath era of 1970-74.

That is the ideological danger: that suspicion of a prime minister who chatted more often than was widely realised by phone to Mr Clinton - their lawyer wives also got on - will make the new president wary of London.

That could rub off on the traditional British role as "the bridge" between the EU and the US, weakening Britain's standing across the Atlantic and the Channel.

Belfast and Dublin will not have the same fascination for a Republican Texan, even if he does have a few debts to pro-Sinn Fein congressmen, as Peter Mandelson denies suggesting.

But, British officials admit, there may be gains, including on international free trade, where Mr Gore was quasi-protectionist.